gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b00000000000000000000000000000000000000000000000000000100000100010000000000010101000101010001000101000101010000000101000101000000 a = 0x00000000000004110015151145405140 a = x⁷⁴ + x⁶⁸ + x⁶⁴ + x⁵² + x⁵⁰ + x⁴⁸ + x⁴⁴ + x⁴² + x⁴⁰ + x³⁶ + x³² + x³⁰ + x²⁶ + x²⁴ + x²² + x¹⁴ + x¹² + x⁸ + x⁶
b = b00000000000000000000000000000000000000000000000000000000010101010000000101010100010001000000010101000101010000000000010101000101 b = 0x00000000000000550154440545400545 b = x⁷⁰ + x⁶⁸ + x⁶⁶ + x⁶⁴ + x⁵⁶ + x⁵⁴ + x⁵² + x⁵⁰ + x⁴⁶ + x⁴² + x³⁴ + x³² + x³⁰ + x²⁶ + x²⁴ + x²² + x¹⁰ + x⁸ + x⁶ + x² + 1
100000100010000000000010101000101010001000101000101010000000101000101000000 | 10101010000000101010100010001000000010101000101010000000000010101000101 - 10101010000000101010100010001000000010101000101010000000000010101000101 | 1 --------------------------------------------------------------------------- | 1010000010001010101010001010101010100010100010001010000000000010100010000 | - 00000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 10101010000000101010100010001000000010101000101010000000000010101000101 | 1 --------------------------------------------------------------------------- | 101010001000000000000010001010101000000000100010000000001000000000100 | - 00000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 00000000000000000000000000000000000000000000000000000000000000000000000 | 0
c_quotient = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010100 c_quotient = 0x00000000000000000000000000000014 c_quotient = x⁴ + x²
c_remainder = b00000000000000000000000000000000000000000000000000000000000101010001000000000000010001010101000000000100010000000001000000000100 c_remainder = 0x00000000000000151000455004401004 c_remainder = x⁶⁸ + x⁶⁶ + x⁶⁴ + x⁶⁰ + x⁴⁶ + x⁴² + x⁴⁰ + x³⁸ + x³⁶ + x²⁶ + x²² + x¹² + x²